N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae

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dc.contributor.areaMathematicsen_US
dc.contributor.authorBonelli, Giulio
dc.contributor.authorMaruyoshi, Kazunobu
dc.contributor.authorTanzini, Alessandro
dc.contributor.authorYagi, Futoshi
dc.date.accessioned2013-04-04T10:56:22Z
dc.date.available2013-04-04T10:56:22Z
dc.date.issued2013-02-05
dc.description33 pages, 1 figure; v2: discussions on U(1) gauge theory and Frenkel-Kac construction have been added in section 5.1, and typos corrected; v3: published version; v4: typos correcteden_US
dc.description.abstractWe compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities C^2/\Gamma in terms of blow-up formulae. We discuss the expansion of the partition function in the \epsilon_1,\epsilon_2 \to 0 limit along with its modular properties and how to derive them from the M-theory perspective. On the two-dimensional conformal field theory side, our results can be interpreted in terms of representations of the direct sum of Heisenberg plus W_N-algebrae with suitable central charges, which can be computed from the fan of the resolved toric variety.We provide a check of this correspondence by computing the central charge of the two-dimensional theory from the anomaly polynomial of M5-brane theory. Upon using the AGT correspondence our results provide a candidate for the conformal blocks and three-point functions of a class of the two-dimensional CFTs which includes parafermionic theories.en_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/6577
dc.language.isoenen_US
dc.miur.area-1en_US
dc.publisherSISSAen_US
dc.relation.ispartofseriesarXiv:1208.0790;
dc.relation.ispartofseriesSISSA preprint;23/2012/EP-FM
dc.rightsSISSAen_US
dc.titleN=2 gauge theories on toric singularities, blow-up formulae and W-algebraeen_US
dc.typePreprinten_US
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